{"id":"https://openalex.org/W7221802207","doi":"https://doi.org/10.48550/arxiv.2610.13955","title":"Certified Geometry and Admissible Motion of Gerver's Sofa","display_name":"Certified Geometry and Admissible Motion of Gerver's Sofa","publication_year":2026,"publication_date":"2026-08-19","ids":{"openalex":"https://openalex.org/W7221802207","doi":"https://doi.org/10.48550/arxiv.2610.13955"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.13955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13955","pdf_url":"https://arxiv.org/pdf/2610.13955","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.13955","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147405539","display_name":"Dawid Trela","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210150966","display_name":"War Studies Academy","ror":"https://ror.org/05113d564","country_code":"PL","type":"education","lineage":["https://openalex.org/I4210150966"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Trela, Dawid","raw_affiliation_strings":["Doctoral School , War Studies University , Warsaw , Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Doctoral School , War Studies University , Warsaw , Poland","institution_ids":["https://openalex.org/I4210150966"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5147405539"],"corresponding_institution_ids":["https://openalex.org/I4210150966"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.329800009727478,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.329800009727478,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.18619999289512634,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.1746000051498413,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/certified-computation","display_name":"certified computation","score":0.6060000061988831},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"interval arithmetic","score":0.7490000128746033},{"id":"https://openalex.org/keywords/contact-curves","display_name":"contact curves","score":0.40299999713897705},{"id":"https://openalex.org/keywords/switching-parameters","display_name":"switching parameters","score":0.3959999978542328},{"id":"https://openalex.org/keywords/support-functions","display_name":"support functions","score":0.45100000500679016},{"id":"https://openalex.org/keywords/exact-rational-arithmetic","display_name":"exact rational arithmetic","score":0.5450000166893005},{"id":"https://openalex.org/keywords/variational-framework","display_name":"variational framework","score":0.3799999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6420000195503235},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.5101000070571899},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.42170000076293945},{"id":"https://openalex.org/C139609574","wikidata":"https://www.wikidata.org/wiki/Q2273509","display_name":"Transcendental equation","level":3,"score":0.4172999858856201},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.41190001368522644},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.39629998803138733},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.3817000091075897},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.350600004196167},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33070001006126404},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2985999882221222},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29339998960494995},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.28369998931884766},{"id":"https://openalex.org/C2776055716","wikidata":"https://www.wikidata.org/wiki/Q7316893","display_name":"Retract","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2630000114440918},{"id":"https://openalex.org/C74544821","wikidata":"https://www.wikidata.org/wiki/Q1783105","display_name":"Contact geometry","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C2778478883","wikidata":"https://www.wikidata.org/wiki/Q7825025","display_name":"Topological complexity","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.13955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13955","pdf_url":"https://arxiv.org/pdf/2610.13955","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.13955","doi":"https://doi.org/10.48550/arxiv.2610.13955","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.13955","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.13955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13955","pdf_url":"https://arxiv.org/pdf/2610.13955","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221802207.pdf","grobid_xml":"https://content.openalex.org/works/W7221802207.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1507872748","https://openalex.org/W1532036648","https://openalex.org/W1996256003","https://openalex.org/W2170345902","https://openalex.org/W2472636575","https://openalex.org/W2697166564","https://openalex.org/W4405031542"],"related_works":["https://openalex.org/W7213664181","https://openalex.org/W4405031542","https://openalex.org/W7124282708","https://openalex.org/W7161512142","https://openalex.org/W7116974567","https://openalex.org/W2472636575","https://openalex.org/W1836602868","https://openalex.org/W2697166564","https://openalex.org/W4399794479","https://openalex.org/W4402326206"],"abstract_inverted_index":{"The":[0,164],"moving":[1],"sofa":[2],"problem":[3],"asks":[4],"for":[5],"the":[6,22,51,59,85,90,107,143,146,180,195],"largest":[7,23],"planar":[8],"set":[9],"that":[10,124,132],"can":[11],"pass":[12],"through":[13,84,142],"a":[14,46,135,178],"unit-width":[15],"right-angled":[16],"hallway.":[17],"Gerver's":[18,160],"1992":[19],"construction":[20],"remains":[21],"explicit":[24,78],"example,":[25],"but":[26],"its":[27],"defining":[28],"switching":[29,61],"parameters,":[30],"continuum":[31],"of":[32,50,159],"supporting":[33,114],"hallways,":[34],"and":[35,41,73,103,129,131,149,173],"contact":[36,74],"topology":[37],"involve":[38],"transcendental":[39],"equations":[40,75],"global":[42,93],"inequalities.":[43],"We":[44,152],"give":[45],"reproducible":[47],"exact-rational":[48],"certification":[49],"construction.":[52],"A":[53],"strict":[54],"four-dimensional":[55],"Krawczyk":[56,67],"inclusion":[57],"encloses":[58],"reduced":[60],"system,":[62],"while":[63],"an":[64,77],"independent":[65],"twenty-two-dimensional":[66],"calculation":[68],"verifies":[69],"Romik's":[70,157],"full":[71],"matching":[72],"in":[76,138,184],"rational":[79,175],"box.":[80],"Exact":[81],"interval":[82],"propagation":[83],"five":[86],"analytic":[87],"phases":[88],"proves":[89],"support":[91,109],"identities,":[92],"half-plane":[94],"constraints,":[95],"inner-wall":[96],"separation,":[97],"niche":[98],"topology,":[99],"oriented":[100],"contacts,":[101],"injectivity,":[102],"area":[104],"bounds.":[105],"From":[106],"certified":[108],"functions":[110],"we":[111,121,192],"identify":[112,154],"every":[113],"hallway":[115],"as":[116],"L_t=x(t)+R_tL.":[117],"For":[118],"G=K_0\\setminus\\mathcal":[119],"N(K_0)":[120],"prove":[122],"directly":[123],"G":[125,141,155],"is":[126,134],"nonempty,":[127],"closed,":[128],"connected":[130],"\u03a6_t(q)=R_{-t}(q-x(t))":[133],"continuous":[136],"path":[137],"SE(2)":[139],"carrying":[140],"hallway,":[144],"with":[145,156],"correct":[147],"initial":[148],"final":[150],"arms.":[151],"further":[153],"reconstruction":[158],"classical":[161],"eighteen-piece":[162],"sofa.":[163],"deterministic":[165],"companion":[166],"verifier":[167],"uses":[168],"only":[169],"Python's":[170],"standard":[171],"library":[172],"exact":[174],"arithmetic.":[176],"As":[177],"consequence,":[179],"Gerver-specific":[181],"geometric":[182],"hypotheses":[183],"Baek's":[185],"recent":[186],"variational":[187],"framework":[188],"are":[189],"rigorously":[190],"certified;":[191],"also":[193],"clarify":[194],"one-sided":[196],"tangent-speed":[197],"convention":[198],"at":[199],"two":[200],"contact-curve":[201],"junctions.":[202]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}